and \(A_n=C n^{-1} \log n\) . The event \(\Omega _0=\left\lbrace \left|\bar{X}^{(n)}(0)-x(0)\right| \le \delta \right\rbrace \)  occurs with
high probability as \(\bar{X}^{(n)}(0) \stackrel{p}{\longrightarrow }x(0)\)  as \(n \rightarrow \infty \) . By [1]}, Theorem 4.1,
\({\rm P}\left(\sup _{0 \le t \le t_0} \left|\bar{X}^{(n)}(t)-x(t)\right|>\epsilon \right) \le \frac{4 A_n}{\delta ^2}+{\rm P}(\Omega _0^c\cup \Omega _1^c \cup \Omega _2^c)\) 
